Structural Engineering 2 and Group Design 2015/16 PDF

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I.D. Number _____________________________ Desk No __________________

Faculty of Science, Engineering and Computing Undergraduate Regulations April/May Examinations 2015/2016 Level 6 MODULE:

CE6013: Structural Engineering 2 and Group Design

DURATION:

Three Hours Instructions to Candidates

This paper contains SIX questions in TWO sections: Sections A and B Answer FOUR questions only Section A: Section B: AND

Answer ONE question Answer ONE question Answer TWO further questions from EITHER Section A OR Section B

All questions carry equal marks THIS PAPER MUST BE HANDED IN AT THE END OF THIS EXAMINATION CANDIDATES ARE PERMITTED TO BRING ONE APPROVED CALCULATOR INTO THIS EXAMINATION: from either Casio FX83 or Casio FX85 series (with any suffix), FX115MS, FX570ES or FX991ES Invigilators are under instruction to remove any other calculators Candidates are reminded that the major steps in all arithmetical calculations are to be set out clearly. Stationery Attached Supplied

Salmon Answer Book Structural Analysis Data Sheet (1 Page) Design Extracts

0

Number of Pages: 1 – 6 + Structural Analysis Data Sheet (1 Page) SECTION A 1. A rigid joint plane frame with two uniformly distributed loads is shown in Figure Q1. Joints are numbered and members are labelled as shown. Joint 1 is a propped support and joints 3 and 4 are fixed supports. Member a carries 10 kN/m and member b carries 6 kN/m. Using Stiffness Matrix Method, (a)

determine the Structure’s Stiffness Matrix, (17 marks)

(b)

calculate the load vector, (6 marks)

(c)

state the displacement vector. (2 marks)

For all members in Figure Q1, the value of a member’s stiffness sub-matrix, K11, is given as  80 0 0    K11 =  0 6 15  x 104  0 15 20

in N and m units

3m 4 c

4m 10 kN/m 1

6 kN/m

a

2

5m

b 7m

Figure Q1

1

3

2

Continued… A rigid joint plane frame with one vertical point load, an applied moment and two uniformly distributed loads is shown in Figure Q2. Joints are numbered and members are labelled as shown. Joints 1 and 4 are fixed supports. The point load is at joint 2 and the applied moment is at joint 3. The uniformly distributed loads are on member a and member c. The relative flexural stiffness for the members is shown in Figure Q2. Considering the flexural deformation only and using the stiffness method, analyse the frame and (a) determine the unknown joint displacements, (13 marks) (b) determine all member end forces, and (7 marks) (c) draw the bending moment diagram for the frame, showing all moments at joints. (Values for maximum sagging bending moments are not required.) (5 marks)

15kNm 3

10 kN

a

2EI

c 2EI

b 2

8m

4m

Figure Q2

2

4 3m

EI

5 kN/m 1

6 kN/m

4m

Continued… A rigid-jointed sway frame is shown in Figure Q3 in which the relative EI values and the applied loading are given. Use the moment distribution method to:

3.

(a)

Determine the Distribution factors for all spans. (3 marks)

(b)

Calculate the final bending moments. (16 marks)

(c)

Plot the bending moment diagram. (3 marks)

(d)

Sketch the deflected shape qualitatively. (3 marks)

The fixed end beams’ solutions are given in the Structural Analysis Data Sheet at the end of the examination script.

80 kN

8kN/m

B

EI

C

EI 8.0 m

A 5.0 m

4.0 m

Figure Q3

3

5.0 m

Continued… SECTION B 4.

Design the steel beam shown in Figure Q4 for shear, bending and Lateral Torsional Buckling (LTB) effects for sagging between points B and C. The loading generally consists of two types of Uniformly Distributed Load (UDL), acting between points A and B and points B and C correspondingly. The unfactored UDL for both parts is 25 kN/m permanent load and 20 kN/m variable load. The positioning of the variable load and the partial safety factors depend on the chosen loadcase. Perform the following design calculations based on EC3: (a)

Choose an appropriate loadcase for maximum sagging moment to occur at mid-span and calculate the loads at Ultimate Limit State (ULS) using appropriate load factors. Calculate the support reactions. Draw shear force and bending moment diagrams for the above mentioned loadcase indicating all significant values. (6 marks)

(b)

Choose an appropriate S275 steel Universal Beam (UB) or Universal Column (UC) section which may be used to resist the maximum bending and shear between points A and B. Check the classification of the section. (5 marks)

(c)

Check shear and bending resistance at ULS. (6 marks)

(d)

Check the LTB effects between the supports at ULS assuming laterally restrained compression flange at the supports and at the end of the cantilever. The flanges are free to rotate in plan between the supports and the loading conditions are normal. (8 marks)

Figure Q4

4

5.

Continued… A 3-span continuous reinforced concrete flanged beam has a cross-section as shown in Figure Q5 and supports slabs of 4.5m span either side. The beam is supported by 250mm square columns. The characteristic values of the permanent and variable loads are g k=25kN/m and qk=20kN/m. Characteristic material strengths are fck = 30MPa and fyk = 500MPa. Main reinforcing bars are H20, links H8 and cover to reinforcement 25mm. Using EN 1992-1-1, carry out the following: (a)

Calculate the total design load on the beam and the Bending Moments at the middle of the interior span. Design the beam for bending at the middle of the interior span and propose suitable reinforcement. (9 marks)

(b)

Calculate the total design load on the beam and the Bending Moments at the 1st interior support. Design the beam for bending at the 1 st interior support and propose suitable reinforcement. (9 marks)

(c)

Calculate the max Shear at the 1st interior support. Design the beam for max shear at the 1st interior support and propose suitable reinforcement. (7 marks)

5

Figure Q5

6.

Continued… A glulam beam of length 7m, cross section of 115 mm x 450 mm and class GL24h, functions under service class 2 conditions. The beam is subjected to a UDL of gk=2kN/m permanent load and qk=3.75kN/m variable load as indicated in Figure Q6. The loads are considered as a medium term action. The beam is laterally torsionally restrained only at the supports. (a) Calculate the maximum bending moment at the ULS at midspan, the design bending strength and the bending stress of the beam (5 marks) (b) Calculate the relative slenderness of the section for bending and the lateral stability factor kcrit. Check if the beam has a sufficient bending strength with the lateral torsional buckling effects taken into account. (12 marks) (c) Carry out a SLS check of the deflection of the beam if the limiting value for the maximum deflection is span/500. (8 marks)

Figure Q6

END OF THE EXAMINATION PAPER

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